SRC/DEPRECATED/ztzrqf.f(3)

NAME
SRC/DEPRECATED/ztzrqf.f

SYNOPSIS

  Functions/Subroutines
subroutine ztzrqf (m, n, a, lda, tau, info)
ZTZRQF

Function/Subroutine Documentation

  subroutine ztzrqf (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, integer info)

ZTZRQF

Purpose:

    !>
    !> This routine is deprecated and has been replaced by routine ZTZRZF.
    !>
    !> ZTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
    !> to upper triangular form by means of unitary transformations.
    !>
    !> The upper trapezoidal matrix A is factored as
    !>
    !>    A = ( R  0 ) * Z,
    !>
    !> where Z is an N-by-N unitary matrix and R is an M-by-M upper
    !> triangular matrix.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= M.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the leading M-by-N upper trapezoidal part of the
    !>          array A must contain the matrix to be factorized.
    !>          On exit, the leading M-by-M upper triangular part of A
    !>          contains the upper triangular matrix R, and elements M+1 to
    !>          N of the first M rows of A, with the array TAU, represent the
    !>          unitary matrix Z as a product of M elementary reflectors.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,M).
    !>

    TAU

    !>          TAU is COMPLEX*16 array, dimension (M)
    !>          The scalar factors of the elementary reflectors.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The  factorization is obtained by Householder's method.  The kth
    !>  transformation matrix, Z( k ), whose conjugate transpose is used to
    !>  introduce zeros into the (m - k + 1)th row of A, is given in the form
    !>
    !>     Z( k ) = ( I     0   ),
    !>              ( 0  T( k ) )
    !>
    !>  where
    !>
    !>     T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ),
    !>                                                   (   0    )
    !>                                                   ( z( k ) )
    !>
    !>  tau is a scalar and z( k ) is an ( n - m ) element vector.
    !>  tau and z( k ) are chosen to annihilate the elements of the kth row
    !>  of X.
    !>
    !>  The scalar tau is returned in the kth element of TAU and the vector
    !>  u( k ) in the kth row of A, such that the elements of z( k ) are
    !>  in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
    !>  the upper triangular part of A.
    !>
    !>  Z is given by
    !>
    !>     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
    !>

Definition at line 137 of file ztzrqf.f.

Author

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